Solution sets for differential equations and inclusions (Q2911572)

In this excellent book, a comprehensive description of methods concerning the topological structure of fixed point sets and solution sets for differential equations and inclusions is presented. The book contains six chapters, namely four main chapters and two supplementary chapters which contain basic notions for a useful basis of the entire book. Chapter 1 focuses on recently obtained fundamental results concerning the topological structure of single-valued and multi-valued fixed point mappings. The case of non-expansive maps is considered, but also the structure of solutions sets for multi-valued contractions is investigated. This abstract theory plays a key role in the investigation of solution sets of many initial and boundary value problems.NEWLINENEWLINEChapter 2 contains classical known results on the existence theory for Cauchy problems and boundary value problems for ordinary differential equations and inclusions. Such problems are considered on compact and noncompact intervals of the real line.NEWLINENEWLINEIn Chapter 3, some of the results obtained in Chapter 1 are used in order to investigate the topological structure of solution sets for some initial and boundary value problems associated with differential equations and inclusions, extending the classical Kneser-Hukuhara theorems.NEWLINENEWLINEIn Chapter 4, a detailed account of the existence theory together with the investigation of the structure of solution sets of impulsive differential equations and inclusions is presented. This chapter is designed as a survey of some recent results obtained by the authors and others.NEWLINENEWLINEIn Chapter 5, the authors present a concise review of the requisite mathematical background, such as, fundamental facts from geometric topology, homology theory related to the Vietoris mapping theorem and, finally, necessary information about the Lefschetz number is given.NEWLINENEWLINEFinally, in Chapter 6, the authors give an overview of basic notions of multivalued analysis.NEWLINENEWLINEAn extensive bibliography of 476 items (most of them recent) is given at the end of the book. The exposition is clear and almost self-contained. Several examples of applications related to initial and boundary value problems are discussed in details. The book is intended to advanced graduate researchers interested in topological properties of fixed point sets and applications.